| eBook ISBN: | 978-1-4704-0263-1 |
| Product Code: | MEMO/141/672.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
| eBook ISBN: | 978-1-4704-0263-1 |
| Product Code: | MEMO/141/672.E |
| List Price: | $48.00 |
| MAA Member Price: | $43.20 |
| AMS Member Price: | $28.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 141; 1999; 71 ppMSC: Primary 58; 70; Secondary 53
Abstract. We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian \(S^1\)-spaces. Additionally, we show that all these spaces are Kähler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.
ReadershipGraduate students and research mathematicians interested in global analysis, analysis on manifolds, and symplectic geometry.
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Table of Contents
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Chapters
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1. Introduction
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2. Graphs
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3. Metrics
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4. Uniqueness: Graph determines space
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5. Isolated fixed points implies toric variety
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6. Blowing-up
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7. Completing the classification; our spaces are Kähler
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Abstract. We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian \(S^1\)-spaces. Additionally, we show that all these spaces are Kähler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.
Graduate students and research mathematicians interested in global analysis, analysis on manifolds, and symplectic geometry.
-
Chapters
-
1. Introduction
-
2. Graphs
-
3. Metrics
-
4. Uniqueness: Graph determines space
-
5. Isolated fixed points implies toric variety
-
6. Blowing-up
-
7. Completing the classification; our spaces are Kähler
